Problem: $h(n) = 7n^{3}+5n^{2}$ $f(t) = -4t+h(t)$ $g(n) = 3n^{2}+3(h(n))$ $ h(g(-1)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(-1)$ . Then we'll know what to plug into the outer function. $g(-1) = 3(-1)^{2}+3(h(-1))$ To solve for the value of $g$ , we need to solve for the value of $h(-1)$ $h(-1) = 7(-1)^{3}+5(-1)^{2}$ $h(-1) = -2$ That means $g(-1) = 3(-1)^{2}+(3)(-2)$ $g(-1) = -3$ Now we know that $g(-1) = -3$ . Let's solve for $h(g(-1))$ , which is $h(-3)$ $h(-3) = 7(-3)^{3}+5(-3)^{2}$ $h(-3) = -144$